Well, Jirachi's arrival coincides with the arrival of a comet. While having a mystical (psychic) quality in most mythologies, in real life comets are composed of ice and metallic elements (steel). As for doom desire, game freak already has a gen 3 event Pokemon with a base 140 power psychic move (deoxys, psycho boost) so they probably didn't want another. Also, steel is Jirachi's primary type.
Hope this helped